 | C. Davies - 1867 - 342 pages
...exceed two right angles : hence, at least two angles of every triangle must be acuteTHEOREM XVIIII A perpendicular is the shortest line that can be drawn from a given point to a given lineII If any number of lines be drawn from the- same point, those which arc nearest the perpendicular... | |
 | Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...angles, and there remain all the exterior angles equal to four right angles (by ax. 3). QED THEOREM XXI. A perpendicular is the shortest line that can be drawn from a given point to an indefinite line. And, of any other lines drawn from the same point, those that are nearest -the... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...that AF is greater than the diagonal of the square. 21. The perpendicular is the shortest straight line that can be drawn from a given point to a given straight line; and of others, that which is nearer to the perpendicular is less than the more remote;... | |
 | Horatio Nelson Robinson - Geometry - 1868 - 276 pages
...opposite the greater angle, AB is less than AC; and AC may be any line not identical with AB ; therefore a perpendicular is the shortest line that can be drawn from A to the line DE. 2d. As the two angles, ACB and ACD, are together equal to two right angles, (Th. 1),... | |
 | Literary and Philosophical Society of Liverpool - 1870 - 312 pages
...I. 15. After I. 11, he neglects to prove the property analogous to that in III. 7 and 8, viz., " the perpendicular is the shortest line that can be drawn from a given point to a given line ; and of the rest, the line which is nearer to the perpendicular is less than one more remote : also... | |
 | André Darré - 1872 - 226 pages
...MN ; then, drawing PD, AP and AD are both perpendicular to PD (124), which is absurd (21). Cor. ii. A perpendicular is the shortest line that can be drawn from a given point to a plane ; for AP is less than any line such as AE drawn from the point A to the plane MN (48). Hence,... | |
 | Euclid, Charles Peter Mason - Geometry - 1872 - 216 pages
...their vertices, when produced, will bisect the base and be at right angles to it. (I. 1-8.) 16. The perpendicular is the shortest line that can be drawn from a given point to a given straight line. (1. 1-19.) 17. Of all the lines that can be drawn from a given point to a given straight... | |
 | Euclides - 1874 - 342 pages
...that shall be bisected by another given straight line. 11. The perpendicular is the shortest straight line that can be drawn from a given point to a given straight line ; and of others, that which is nearer to the perpendicular is less than the more remote... | |
 | Thomas Hunter - Geometry, Plane - 1878 - 142 pages
...right angles, if the angles are all equal each must be a right angle. PROPOSITION XXXI.—THEOREM. A. perpendicular is the shortest line that can be drawn from a given point to a given line; two oblique lines drawn from this point to two points on the line equidistant from the perpendicular... | |
 | Euclides - 1879 - 146 pages
...in H, show that FH, GH are equal. 6. In the same^figure, show that AH bisects the angle BAG. 7. The perpendicular is the shortest line that can be drawn from a given point to a given line, and that which is nearer to the perpendicular is less than one more remote; and from the same given... | |
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The perpendicular is the shortest straight line that can be drawn from a given point to a given straight line; and... 
